Exact Relations for Two-Photon-Exchange Effect in Elastic $ep$ Scattering by Dispersion Relation and Hadronic Model

TL;DR

This paper derives exact properties and relations for the two-photon-exchange effect in elastic electron-proton scattering, unifying dispersion relation and hadronic models, and providing improved methods for analyzing scattering data.

Contribution

It establishes exact relations between dispersion relation and hadronic model methods for TPE effects, and proposes modified forms that include various interaction contributions.

Findings

Derived exact relations between DR and HM methods.

Modified the methods to include seagull, meson-exchange, contact, and off-shell effects.

Provided new forms for analyzing elastic ep scattering data.

Abstract

The two-photon-exchange (TPE) effect plays a key role to extract the form factors (FFs) of the proton. In this work, we present some exact properties on the TPE effect in the elastic $ep$ scattering based on four types of typical and general interactions. The possible kinematical singularities, the asymptotic behaviors and the branch cuts of the TPE amplitudes are analyzed. The analytic expressions clearly indicate some exact relations between the dispersion relation (DR) method and the hadronic model (HM) method. It suggests that the two methods should be modified to general forms, respectively. After the modifications the new forms give the same results. Furthermore, they automatically and correctly include the contributions due to the seagull interaction, the meson-exchange effect, the contact interactions and the off-shell effect. To analyze the elastic $e^{\pm}p$ scattering data sets, the new forms should be used.